Partial regularity for parabolic systems of double phase type

Fuente: arXiv
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Main Authors: Ok, Jihoon, Scilla, Giovanni, Stroffolini, Bianca
Format: Preprint
Published: 2025
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author Ok, Jihoon
Scilla, Giovanni
Stroffolini, Bianca
author_facet Ok, Jihoon
Scilla, Giovanni
Stroffolini, Bianca
contents We study partial regularity for nondegenerate parabolic systems of double phase type, where the growth function is given by $H(z,s)=s^p+a(z)s^q$, $z=(x,t)\inΩ_T$, with $\tfrac{2n}{n+2}<p\le q$ and $a(z)$ a nonnegative $C^{0,α,\fracα{2}}$-continuous function for some $α\in(0,1]$. As the main result we prove that if $q< \min \{p+\tfrac{αp }{n+2}, p+1 \}$ the spatial gradient of any weak solution is locally Hölder continuous, except on a set of measure zero.
format Preprint
id arxiv_https___arxiv_org_abs_2510_03849
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Partial regularity for parabolic systems of double phase type
Ok, Jihoon
Scilla, Giovanni
Stroffolini, Bianca
Analysis of PDEs
35D30, 35K55, 35K65
We study partial regularity for nondegenerate parabolic systems of double phase type, where the growth function is given by $H(z,s)=s^p+a(z)s^q$, $z=(x,t)\inΩ_T$, with $\tfrac{2n}{n+2}<p\le q$ and $a(z)$ a nonnegative $C^{0,α,\fracα{2}}$-continuous function for some $α\in(0,1]$. As the main result we prove that if $q< \min \{p+\tfrac{αp }{n+2}, p+1 \}$ the spatial gradient of any weak solution is locally Hölder continuous, except on a set of measure zero.
title Partial regularity for parabolic systems of double phase type
topic Analysis of PDEs
35D30, 35K55, 35K65
url https://arxiv.org/abs/2510.03849